If the mount is large (medium sized cavalier) then it takes up 4 spaces. In this case the cavalier can attack as though in any of those 4 squares - which means #1.
If the mount is medium (with a small rider) then #3 - but personally as a GM I'd house rule they get to make their charge attack as well - but by the RAW he loses his charge attack since his target is no longer valid based on weapon range.
Let's first say things precisely: technically, when a character is mounted, they don't charge. Their mount charges, and they just move with its speed and take the same penalty to AC and bonus to the attack roll.
Now, the rules for readying action say:
"If the triggered action is part of another character’s activities, you interrupt the other character. Assuming he is still capable of doing so, he continues his actions once you complete your readied action."
I believe the following things happen:
1. The horse charge is put on hold until the npcs makes his readied action.
2. The NPC move towards the cavalier. When he leaves the square 10 ft. away from the cavalier, they provoke AoO.
3. The cavalier can take the AoO against the NPC.
4. The NPC finishes his move, stopping next to the cavalier.
5. The horse's charge would be resumed. However, the NPC is now standing 5 ft from the horse, which means that the horse's charge ends. The horse can make an attack, but the cavalier can't, because the NPC is too close. Alternatively, if the path ahead is free (which may be, depending on where the NPC will be standing), the cavalier can use Ride-by-Attack and continue moving, but then neither he nor his mount will be able to attack.
So in total it's the option you've listed as 4., although it's to remember that while the cavalier can't make the attack after the charge, the mount still can.
If the mount is large (medium sized cavalier) then it takes up 4 spaces. In this case the cavalier can attack as though in any of those 4 squares - which means #1.
I see this a lot. Where is it stated? AFAIK, you cannot attack with a lance from horseback at 5' range simply by saying "I attack from the rear square".
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Right, but you still can't choose the back corner to attack from to get around the 5' hole in your reach.
d2pfsrd has some diagrams that show what large and larger creatures threaten when wielding a reach weapon or not. A cavalier on a large mount would threaten the orange(peach?) squares and not the green squares.
You threaten 10 feet out from any square on the mount, but not 10 feet across the mount.
Also, when your mount charges, you are also charging, per the FAQ.
Mounted Combat: When making a charge while mounted, which creature charges? The rider or the mount?
Both charge in unison, suffer the same penalty to AC, the gaining the same bonus to the attack rolls and following all other rules for the charge. The mounted combat rules are a little unclear on this. Replace the third paragraph under the "Combat while Mounted" section on page 202 with the following text. Note that a "mounted charge" is synonymous with a "charge while mounted," and that when a lance is "when used from the back of a charging mount" it is during a mounted charge not when only the mount charges.A mounted charge is a charge made by you and your mount. During a mounted charge, you deal double damage with your first melee attack made with a lance or with any weapon if you have Spirited Charge (or a similar effect), or you deal triple damage with a lance and Spirited Charge.
This change will be reflected in future printings of the Pathfinder RPG Core Rulebook
Let's first say things precisely: technically, when a character is mounted, they don't charge. Their mount charges, and they just move with its speed and take the same penalty to AC and bonus to the attack roll.
Those were the rules pre-2014, before they released the Mounted Charge FAQ (quoted above) which changed how mounted charges work.
Nowadays both mount and rider must take the charge action to make it a "Mounted Charge" for effects such as Spirited Charge and Lance bonus damage.****
Also, when your mount charges, you are also charging, per the FAQ.
If you want to make a "Mounted Charge", both rider and mount must take the charge action. But it is possible for the mount to be the only one charging in a turn, as the FAQ uses that scenario as an example of when it isn't a "Mounted Charge".
If the mount is large (medium sized cavalier) then it takes up 4 spaces. In this case the cavalier can attack as though in any of those 4 squares - which means #1.I see this a lot. Where is it stated? AFAIK, you cannot attack with a lance from horseback at 5' range simply by saying "I attack from the rear square".Under mounted combat in the combat section.
A horse (not a pony) is a Large creature and thus takes up a space 10 feet (2 squares) across. For simplicity, assume that you share your mount’s space during combat.
Blaphers and Thune make a good point. I mis-remembered this rule. You are considered the size of the mount. So your attack range is defined by the closest point from you to the target. No charge attack by RAW once they are inside your 5' range.
Is it valid to allow the mount to overrun the fool that decided to stand in front of a charging horse? Since overruns can be performed as part of a charge?
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There’s a difference between interrupting a charge and invalidating a charge, though. A readied action to brace doesn’t invalidate the charge. Once it’s resolved, you can continue the charge as normal. Someone moving into a charge lane between the charging character and their target invalidates the charge. You are no longer charging at that point, because it’s no longer legal to charge (excepting something like charge through). They don’t even have to provoke if all they are wanting to do is stop the charge. They just need to move into the charge lane. If you don’t have a way to continue the charge to your target after that, then the charge is invalidated.
You still take the penalty to AC, because that lasts until your next turn, whether you are still charging or not.
If someone approaches you from the side and provokes without getting into your charge lane, then maybe you’d get x2 damage for the lance, because of the non specific language, as you would still be on a charging mount.
EDIT: Also note per the FAQ quoted above that it has to be a mounted charge to get double damage (you must be charging as well, not just the mount), and that the extra damage only applies to your first attack. So if you have pounce, you don’t get double damage on all of your attacks at the end of the charge. And, if you’re going to give double damage on the AoO, then you won’t get double damage if you’re able to continue the charge and make an attack against your original opponent.